The regulations governing Qualified Teacher Status state that it never expires. Even if a teacher leaves the profession or retires, even if a teacher is debarred from the profession for some reason, QTS cannot be revoked. (So QTS is necessary but not sufficient. If you're banned from teaching then you can't do it, but this doesn't make you no longer a qualified teacher.)

And if the status never expires, then I reckon it still obtains after death.